Preheat your oven to 180℃ (356℉) and line a 7.5" square baking tin with parchment paper.
Make blackberry jam*. In a medium saucepan over low-medium heat, add 240 g blackberries, 100 g white sugar, and 1 tablespoon lemon juice. Cook, stirring constantly, until the mixture becomes thick and jammy. This may take around 15 minutes. Remove from the heat and set aside; the jam will thicken as it cools.
Make the cake batter. First, beat 125 ml olive oil and 200 g white sugar until well combined. Next, add 4 eggs one by one, whisking after each egg. Finally, sift in the dry ingredients: 120 g ground almonds, 60 g plain flour, and ½ teaspoon baking powder. Using a wooden spoon or spatula, fold the dry ingredients into the batter.
Pour the batter into the cake tin and use a spoon to swirl 3 tablespoons blackberry jam into the batter.
Bake the blackberry almond cake for about 60-70 minutes, on the middle shelf of your oven. Cover the top shelf with a pan so the cake is not directly exposed (otherwise the top will burn)**. You'll know it's done when a skewer comes out clean.
Make the mascarpone icing. In a large mixing bowl, beat 80 g double cream until it's light, fluffy, and thickened. Next, add 250 g mascarpone cheese and 40 g icing sugar. Whisk again until everything is incorporated, no more. Swirl through 2 tablespoons blackberry jam — enough so that some parts of the icing remain white.
Let the cake cool, then spread over the icing. Optionally, top the cake with more fresh blackberries and slivered almonds.
Notes
* You can skip this step and use pre-made, store-bought blackberry jam to save time if preferred.